1. University of Hail Electric Circuits EE 202
Professor / Mohamed A H Eleiwa

3. Summary Example-1 Scientific and Engineering Notation
Very large and very small numbers are represented with scientific and engineering notation.
Example-1
47,000,000 = 4.7 x 107 (Scientific Notation)
= 47 x 106 (Engineering Notation)

4. Summary Example-2 Example-3 Scientific and Engineering Notation
= 2.7 x 10-5 (Scientific Notation)
= 27 x 10-6 (Engineering Notation)
Example-3
0.605 = 6.05 x 10-1 (Scientific Notation)
= 605 x 10-3 (Engineering Notation)

5. Summary Metric Conversions
Numbers in scientific notation can be entered in a scientific calculator using the EE key.
Most scientific calculators can be placed in a mode that will automatically convert any decimal number entered into scientific notation or engineering notation.

6. Summary SI Fundamental Units Quantity Unit Symbol Length Meter m
Kilogram kg
Second s
Ampere A
Kelvin K
Candela cd
Mole mol
Mass
Time
Electric current
Temperature
Luminous intensity
Amount of substance

7. Summary Some Important Electrical Units
Except for current, all electrical and magnetic units are derived from the fundamental units. Current is a fundamental unit.
Quantity Unit Symbol
Current
Ampere A
Coulomb C
Volt V
Ohm W
Watt W
Charge
These derived units are based on fundamental units from the meter-kilogram-second system, hence are called mks units.
Voltage
Resistance
Power

8. Summary Large Engineering Metric Prefixes P T G M k peta tera giga
mega
kilo
1015
1012
109
106
103
Can you name the prefixes and their meaning?

9. Summary Small Engineering Metric Prefixes m n p f milli micro nano
pico
femto
10-3
10-6
10-9
10-12
10-15
Can you name the prefixes and their meaning?

10. Summary Example-1 Metric Conversions Smaller unit 0.47 MW = 470 kW
When converting from a larger unit to a smaller unit, move the decimal point to the right. Remember, a smaller unit means the number must be larger.
Smaller unit
Example-1
0.47 MW = 470 kW
Larger number

11. Summary Example-2 Metric Conversions Larger unit 10,000 pF = 0.01 mF
When converting from a smaller unit to a larger unit, move the decimal point to the left. Remember, a larger unit means the number must be smaller.
Larger unit
Example-2
10,000 pF = 0.01 mF
Smaller number

12. Summary Example-1 Metric Arithmetic 10,000 W + 22 kW =
When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.
Example-1
10,000 W + 22 kW =
10,000 W + 22,000 W = 32,000 W
Alternatively,
10 kW + 22 kW = 32 kW

13. Summary Example-2 Metric Arithmetic 200 mA + 1.0 mA =
When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.
Example-2
200 mA mA =
200 mA + 1,000 mA = 12,000 mA
Alternatively,
0.200 mA mA = 1.2 mA

14. Summary Voltage The defining equation for voltage is
One volt is the potential difference (voltage) between two points when one joule of energy is used to move one coulomb of charge from one point to the other.

15. Summary Question: Current
Current (I) is the amount of charge (Q) that flows past a point in a unit of time (t). The defining equation is:
One ampere is a number of electrons having a total charge of 1 C moving through a given cross section in 1 s.
Question:
What is the current if 2 C passes a point in 5 s?
0.4 A

16. Summary Resistance Resistance is the opposition to current.
One ohm (1 W) is the resistance if one ampere (1 A) is in a material when one volt (1 V) is applied.
Conductance is the reciprocal of resistance.
Components designed to have a specific amount of resistance are called resistors.

17. Summary Resistance color-code Resistance value, first three bands:
First band – 1st digit
Second band – 2nd digit
*Third band – Multiplier (number of
zeros following second digit)
Fourth band - tolerance
* For resistance values less than 10 W, the third band is either gold or silver. Gold is for a multiplier of 0.1 and silver is for a multiplier of 0.01.

18. Summary
Question
What is the resistance and tolerance of each of the four-band resistors?
5.1 kW ± 5%
820 kW ± 5%
47 W ± 10%
1.0 W ± 5%

19. Summary Alphanumeric Labeling
Two or three digits, and one of the letters R, K, or M are used to identify a resistance value.
The letter is used to indicate the multiplier, and its position is used to indicate decimal point position.

20. Summary Variable resistors
Variable resistors include the potentiometer and rheostat. The center terminal of a variable resistor is connected to the wiper. R
Variable resistor (potentiometer) R
To connect a potentiometer as a rheostat, one of the outside terminals is connected to the wiper.
Variable resistor (rheostat)

21. Summary The electric circuit
Circuits are described pictorially with schematics. For example, the flashlight can be represented by
Switch
Battery (2 cells)
Lamp

22. Summary
The DMM VW
The DMM (Digital Multimeter) is an important multipurpose instrument which can measure voltage, current, and resistance. Many include other measurement options.

23. Summary
Analog meters
An analog multimeter is also called a VOM (volt-ohm-milliammeter). Analog meters measure voltage, current, and resistance. The user must choose the range and read the proper scale.
Photo courtesy of Triplett Corporation

24. Summary Review of V, I, and R
the amount of energy per charge available to
move electrons from one point to another in a circuit and is measured in volts.
Voltage is
the rate of charge flow and is measured in
amperes.
Current is
the opposition to current and is measured
in ohms.
Resistance is

25. Summary Question: Ohm’s law
The most important fundamental law in electronics is Ohm’s law, which relates voltage, current, and resistance.
Georg Simon Ohm ( ) formulated the equation that bears his name:
Question:
What is the current in a circuit with a 12 V source if the resistance is 10 W?
1.2 A

26. Summary Question: Ohm’s law
If you need to solve for voltage, Ohm’s law is:
Question:
What is the voltage across a 680 W resistor if the current is 26.5 mA?
18 V

27. Summary Question: Ohm’s law
If you need to solve for resistance, Ohm’s law is:
What is the (hot) resistance of the bulb?
Question:
115 V
132 W

28. Summary Energy and Power
In electrical work, the rate energy is dissipated can be determined from any of three forms of the power formula.
Together, the three forms are called Watt’s law.

29. Summary Energy and Power Example-1: Solution:
What power is dissipated in a 27 W resistor is the current is A?
Solution:
Given that you know the resistance and current, substitute the values into P =I 2R.

30. Summary Summary Series circuits
All circuits have three common attributes. These are:
1. A source of voltage.
2. A load.
3. A complete path.

31. Summary Summary A series circuit is one that has
Series circuits
A series circuit is one that has
only one current path. R1 R1 R2 VS R2 VS R1 R2 R3 VS R3 R3

32. Summary
Summary
Series circuit rule for current:
Because there is only one path, the current everywhere is
the same.
2.0 mA
For example, the reading on the first ammeter is 2.0 mA, What do the other meters read?
2.0 mA
2.0 mA
2.0 mA

33. Summary Summary The total resistance of resistors in series is
Series circuits
The total resistance of resistors in series is
the sum of the individual resistors.
For example, the resistors in a series circuit are 680 W, 1.5 kW, and 2.2 kW. What is the total resistance?
4.38 kW

34. Summary Summary Summary
Series circuit
Tabulating current, resistance, voltage and power is a useful way to summarize parameters in a series circuit.
Continuing with the previous example, complete the parameters listed in the Table.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 4.38 kW VS= 12 V PT=
2.74 mA
1.86 V
5.1 mW
2.74 mA
4.11 V
11.3 mW
2.74 mA
6.03 V
16.5 mW
2.74 mA
32.9 mW

35. Summary
Summary
Voltage sources in series
Voltage sources in series add algebraically. For example, the total voltage of the sources shown is
27 V
What is the total voltage if one battery is accidentally reversed?
Question:
9 V

36. Summary Summary Kirchhoff’s voltage law
Kirchhoff’s voltage law (KVL) is generally stated as:
The sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that closed path.
KVL applies to all circuits, but you must apply it to only one closed path. In a series circuit, this is (of course) the entire circuit.
A mathematical shorthand way of writing KVL is

37. Summary Summary Kirchhoff’s voltage law
Notice in the series example given earlier that the sum of the resistor voltages is equal to the source voltage.
I1= R1= 0.68 kW V1= P1=
2.74 mA
1.86 V
5.1 mW
I2= R2= 1.50 kW V2= P2=
2.74 mA
4.11 V
11.3 mW
I3= R3= 2.20 kW V3= P3=
2.74 mA
6.03 V
16.5 mW
IT= RT= 4.38 kW VS= 12 V PT=
2.74 mA
32.9 mW

38. Summary Summary Voltage divider rule
The voltage drop across any given resistor in a series circuit is equal to the ratio of that resistor to the total resistance, multiplied by source voltage.
Assume R1 is twice the size of R2. What is the voltage across R1?
Question:
8 V

39. Summary Summary Voltage divider What is the voltage across R2?
Example:
What is the voltage across R2?
Solution:
The total resistance is 25 kW.
Notice that 40% of the source voltage is across R2, which represents 40% of the total resistance.
Applying the voltage divider formula:
8.0 V

40. Summary Summary Resistors in parallel
Resistors that are connected to the same two points are said to be in parallel.

41. Summary Summary Parallel circuits
A parallel circuit is identified by the fact that it has
more than one current path (branch) connected to a common voltage source.

42. Summary Summary Parallel circuit rule for voltage
Because all components are connected across the same voltage source, the voltage across each is the same.
For example, the source voltage is 5.0 V. What will a volt- meter read if it is placed across each of the resistors?

43. Summary Summary Parallel circuit rule for resistance
The total resistance of resistors in parallel is
the reciprocal of the sum of the reciprocals of the individual resistors.
For example, the resistors in a parallel circuit are 680 W, 1.5 kW, and 2.2 kW. What is the total resistance?
386 W

44. Summary Summary Special case for resistance of two parallel resistors
The resistance of two parallel resistors can be found by
either: or
Question:
What is the total resistance if R1 = 27 kW and R2 = 56 kW?
18.2 kW

45. Summary Summary Parallel circuit
Tabulating current, resistance, voltage and power is a useful way to summarize parameters in a parallel circuit.
Continuing with the previous example, complete the parameters listed in the Table.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 386 W VS= 5.0 V PT=
7.4 mA
5.0 V
36.8 mW
3.3 mA
5.0 V
16.7 mW
2.3 mA
5.0 V
11.4 mW
13.0 mA
64.8 mW

46. Summary Summary Kirchhoff’s current law
Kirchhoff’s current law (KCL) is generally stated as:
The sum of the currents entering a node is equal to the sum of the currents leaving the node.
Notice in the previous example that the current from the source is equal to the sum of the branch currents.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 386 W VS= 5.0 V PT=
5.0 V
13.0 mA
2.3 mA
3.3 mA
7.4 mA
36.8 mW
16.7 mW
11.4 mW
64.8 mW

47. Summary Summary Current divider
When current enters a node (junction) it divides into currents with values that are inversely proportional to the resistance values.
and
The most widely used formula for the current divider is the two-resistor equation. For resistors R1 and R2,
Notice the subscripts. The resistor in the numerator is not the same as the one for which current is found.

48. Summary Summary Example Solution Current divider
Assume that R1is a 2.2 kW resistor that is in parallel with R2, which is 4.7 kW. If the total current into the resistors is 8.0 mA, what is the current in each resistor?
Solution
5.45 mA
2.55 mA
Notice that the larger resistor has the smaller current.

49. Summary Summary Power in parallel circuits Question:
Power in each resistor can be calculated with any of the standard power formulas. Most of the time, the voltage is
known, so the equation
is most convenient.
As in the series case, the total power is the sum of the powers dissipated in each resistor.
Question:
What is the total power if 10 V is applied to the parallel combination of R1 = 270 W and R2 = 150 W?
1.04 W

50. Summary Summary Question: Answer: Follow up:
Assume there are 8 resistive wires that form a rear window defroster for an automobile.
(a) If the defroster dissipates 90 W when connected to a 12.6 V source, what power is dissipated by each resistive wire?
(b) What is the total resistance of the defroster?
(a) Each of the 8 wires will dissipate 1/8 of the total power or
Answer:
(b) The total resistance is
Follow up:
What is the resistance of each wire?
1.76 W x 8 = 14.1 W

51. Summary Summary Combination circuits
Most practical circuits have various combinations of series and parallel components. You can frequently simplify analysis by combining series and parallel components.
An important analysis method is to form an equivalent circuit. An equivalent circuit is one that has
characteristics that are electrically the same as another circuit but is generally simpler.

52. Summary
Summary
Kirchhoff’s voltage law and Kirchhoff’s current law can be applied to any circuit, including combination circuits.
So will this path!
For example, applying KVL, the path shown will have a sum of 0 V.

53. Summary
Summary
Kirchoff’s current law can also be applied to the same circuit. What are the readings for node A?

54. Summary Summary Combination circuits
Tabulating current, resistance, voltage and power is a useful way to summarize parameters. Solve for the unknown quantities in the circuit shown.
I1= R1= 270 W V1= P1=
21.6 mA
5.82 V
126 mW
I2= R2= 330 W V2= P2=
12.7 mA
4.18 V
53.1 mW
I3= R3= 470 W V3= P3=
8.9 mA
4.18 V
37.2 mW
IT= RT= VS= 10 V PT=
21.6 mA
464 W
216 mW

55. Summary
Summary
Kirchhoff’s laws can be applied as a check on the answer.
equal to the sum of the branch currents in R2 and R3.
Notice that the current in R1 is
The sum of the voltages around the outside loop is zero.
I1= R1= 270 W V1= P1=
21.6 mA
5.82 V
126 mW
I2= R2= 330 W V2= P2=
12.7 mA
4.18 V
53.1 mW
I3= R3= 470 W V3= P3=
8.9 mA
4.18 V
37.2 mW
IT= RT= VS= 10 V PT=
21.6 mA
464 W
216 mW

56. Summary Summary Thevenin’s theorem
Thevenin’s theorem states that any two-terminal, resistive circuit can be replaced with a simple equivalent circuit when viewed from two output terminals. The equivalent circuit is:

57. Summary Summary Thevenin’s theorem
the open circuit voltage between the two output terminals of a circuit.
VTH is defined as
the total resistance appearing between the two output terminals when all sources have been replaced by their internal resistances.
RTH is defined as

58. Summary Summary Thevenin’s theorem
What is the Thevenin voltage for the circuit?
8.76 V
What is the Thevenin resistance for the circuit?
7.30 kW
Output terminals
Remember, the load resistor has no affect on the Thevenin parameters.

59. Summary Summary Maximum power transfer
The maximum power is transferred from a source to a load when the load resistance is equal to the internal source resistance.
The maximum power transfer theorem assumes the source voltage and resistance are fixed.

60. Summary Summary Example: Solution: Maximum power transfer
What is the power delivered to the matching load?
Solution:
The voltage to the load is 5.0 V. The power delivered is

61. Summary Summary Superposition theorem Example:
The superposition theorem is a way to determine currents and voltages in a linear circuit that has multiple sources by taking one source at a time and algebraically summing the results.
Example:
What does the ammeter read for I2? (See next slide for the method and the answer).

62. Summary Summary What does the ammeter read for I2?
Source 1: RT(S1)= I1= I2=
Source 2: RT(S2)= I3= I2=
Both sources I2=
Set up a table of pertinent information and solve for each quantity listed:
6.10 kW
1.97 mA
0.98 mA
8.73 kW
2.06 mA
0.58 mA
1.56 mA
The total current is the algebraic sum.

63. Node Voltage Method (Nodal Analysis)

70. Summary The Basic Capacitor
Capacitors are one of the fundamental passive components. In its most basic form, it is composed of two conductive plates separated by an insulating dielectric.
The ability to store charge is the definition of capacitance.
Conductors
Dielectric

71. Summary The Basic Capacitor Initially uncharged Source removed
Fully charged
Charging
The charging process…
A capacitor with stored charge can act as a temporary battery.

72. Example Capacitance Capacitance is the ratio of charge to voltage
Rearranging, the amount of charge on a capacitor is determined by the size of the capacitor (C) and the voltage (V).
Example
If a 22 mF capacitor is connected to a 10 V source, the charge is
220 mC

73. Capacitance
A capacitor stores energy in the form of an electric field that is established by the opposite charges on the two plates. The energy of a charged capacitor is given by the equation
where
W = the energy in joules
C = the capacitance in farads
V = the voltage in volts

74. Summary
Capacitance
The capacitance of a capacitor depends on three physical characteristics.
C is directly proportional to
the relative dielectric constant
and the plate area.
C is inversely proportional to
the distance between the plates

75. Summary Example Capacitance
Find the capacitance of a 4.0 cm diameter sensor immersed in oil if the plates are separated by 0.25 mm.
Example
The plate area is
The distance between the plates is
178 pF

76. Summary Series capacitors
When capacitors are connected in series, the total capacitance is smaller than the smallest one. The general equation for capacitors in series is
The total capacitance of two capacitors is
…or you can use the product-over-sum rule

77. Summary Example Series capacitors
If a mF capacitor is connected in series with an 800 pF capacitor, the total capacitance is
444 pF

78. Summary Example Parallel capacitors
When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitors. The general equation for capacitors in parallel is
Example
If a mF capacitor is connected in parallel with an 800 pF capacitor, the total capacitance is
1800 pF

79. Summary The Basic Inductor
One henry is the inductance of a coil when a current, changing at a rate of one ampere per second, induces one volt across the coil. Most coils are much smaller than 1 H.
The effect of inductance is greatly magnified by adding turns and winding them on a magnetic material. Large inductors and transformers are wound on a core to increase the inductance.
Magnetic core

80. Summary Factors affecting inductance
Four factors affect the amount of inductance for a coil. The equation for the inductance of a coil is
where
L = inductance in henries
N = number of turns of wire
m = permeability in H/m (same as Wb/At-m)
l = coil length on meters

81. Summary
Example
What is the inductance of a 2 cm long, 150 turn coil wrapped on an low carbon steel core that is 0.5 cm diameter? The permeability of low carbon steel is 2.5 x10-4 H/m (Wb/At-m).
22 mH

82. Summary Example Series inductors
When inductors are connected in series, the total inductance is the sum of the individual inductors. The general equation for inductors in series is
Example
If a 1.5 mH inductor is connected in series with an 680 mH inductor, the total inductance is
2.18 mH

83. Summary Parallel inductors
When inductors are connected in parallel, the total inductance is smaller than the smallest one. The general equation for inductors in parallel is
The total inductance of two inductors is
…or you can use the product-over-sum rule.

84. Summary Example Parallel inductors
If a 1.5 mH inductor is connected in parallel with an 680 mH inductor, the total inductance is
468 mH

85. OBJECTIVES
Become familiar with the characteristics of a sinusoidal waveform, including its general format, average value, and effective value.
Be able to determine the phase relationship between two sinusoidal waveforms of the same frequency.
Understand how to calculate the average and effective values of any waveform.
Become familiar with the use of instruments designed to measure ac quantities.

86. SINUSOIDAL ac VOLTAGE CHARACTERISTICS AND DEFINITIONS Generation
Sinusoidal ac voltages are available from a variety of sources.
The most common source is the typical home outlet, which provides an ac voltage that originates at a power plant.
Most power plants are fueled by water power, oil, gas, or nuclear fusion.

87. SINUSOIDAL ac VOLTAGE CHARACTERISTICS AND DEFINITIONS Definitions
FIG Important parameters for a sinusoidal voltage.

88. AVERAGE POWER AND POWER FACTOR
Resistor
Inductor
Capacitor
Power Factor

89. AVERAGE POWER AND POWER FACTOR
FIG Purely inductive load with Fp = 0.
FIG Purely resistive load with Fp = 1.

90. COMPLEX NUMBERS
A complex number represents a point in a two-dimensional plane located with reference to two distinct axes.
This point can also determine a radius vector drawn from the origin to the point.
The horizontal axis is called the real axis, while the vertical axis is called the imaginary axis.

91. COMPLEX NUMBERS
FIG Defining the real and imaginary axes of a complex plane.

92. RECTANGULAR FORM
The format for the rectangular form is:

93. POLAR FORM
The format for the polar form is:

94. MATHEMATICAL OPERATIONS WITH COMPLEX NUMBERS
Complex Conjugate
Reciprocal
Addition
Subtraction
Multiplication
Division

95. IMPEDANCE AND THE PHASOR DIAGRAM Resistive Elements
FIG Resistive ac circuit.

96. IMPEDANCE AND THE PHASOR DIAGRAM Resistive Elements
In phasor form,

97. IMPEDANCE AND THE PHASOR DIAGRAM Resistive Elements
FIG Example 15.1.

98. IMPEDANCE AND THE PHASOR DIAGRAM Capacitive Reactance
We learned in Chapter 13 that for the pure capacitor in Fig , the current leads the voltage by 90° and that the reactance of the capacitor XC is determined by 1/ψC.
We have

99. SERIES CONFIGURATION R-L-C
FIG Applying phasor notation to the circuit in Fig

100. VOLTAGE DIVIDER RULE
FIG Example

101. FREQUENCY RESPONSE FOR SERIES ac CIRCUITS Series R-C ac Circuit
FIG Determining the frequency response of a series R-C circuit.

102. ILLUSTRATIVE EXAMPLES
FIG Example 16.1.

103. ILLUSTRATIVE EXAMPLES
FIG Network in Fig after assigning the block impedances.

104. ILLUSTRATIVE EXAMPLES
FIG Network in Fig after assigning the block impedances.
FIG Example 16.2.

105. Δ-Y, Y-Δ CONVERSIONS
The Δ-Y, Y-Δ (or p-T, T-p as defined in Section 8.12) conversions for ac circuits are not derived here since the development corresponds exactly with that for dc circuits.
FIG Δ-Y configuration.

106. Δ-Y, Y-Δ CONVERSIONS
FIG The T and π configurations.

107. Δ-Y, Y-Δ CONVERSIONS
FIG Converting the upper Δ of a bridge configuration to a Y.

108. Δ-Y, Y-Δ CONVERSIONS
FIG The network in Fig following the substitution of the Y configuration.

109. Δ-Y, Y-Δ CONVERSIONS
FIG Example

110. Δ-Y, Y-Δ CONVERSIONS
FIG Converting a Δ configuration to a Y configuration.

111. Δ-Y, Y-Δ CONVERSIONS
FIG Substituting the Y configuration in Fig into the network in Fig

112. Δ-Y, Y-Δ CONVERSIONS
FIG Converting the Y configuration in Fig to a Δ.

113. Δ-Y, Y-Δ CONVERSIONS
FIG Substituting the Δ configuration in Fig into the network in Fig